Physical properties of calcium aluminates from vibrational spectroscopy

Heat capacity (C_V) and entropy (S) as a function of temperature were calculated for phases in the CaO-Al₂O₃ system from vibrational spectra using a quasi-harmonic model. Calculated values of C_V at 298 K for the calcium aluminates may have uncertainties as small as ±1%, based on comparison with published calorimetric data for CaO, Al₂O₃, and CaAl₂O₄. For hibonite (CaAl₁₂O₁₉), we predict C_P as 519.3 J/mol-K and S as 391.7 J/mol-K, at 298 K. For grossite (CaAl₄O₇), calculated values of C_P as 195.9 J/mol-K and of S as 172.0 J/mol-K are slightly smaller than the available calorimetric data at 298 K, consistent with calorimetric data having been obtained from samples containing ∼10 wt% hibonite impurities. Thermal conductivity at 298 K (k₀) is predicted from peak widths of the vibrational modes using the damped harmonic oscillator model of a phonon gas. Calculations of k₀ for CaO and Al₂O₃ differ from the measurements by 17% and 5%, respectively. The discrepancy for lime is larger due to uncertainties in its peak widths. This comparison suggests that our results for the calcium aluminates should be more accurate than conventional measurements of k₀ which are commonly uncertain by ∼25%.     

Evaluation of thermochemical data on Fe-Mg olivine,orthopyroxene, spinel and Ca-Fe-Mg-Al garnet

Thermochemical data on Fe-Mg olivine, orthopyroxene, spinel and Ca-Fe-Mg garnet have been tested and reevaluated in reproducing experimental equilibrium data. All data (except of spinel) adjusted in this process lie within the error limits of original calorimetric experiments. For spinel, an enthalpy of −2307.2 kJ/mol and an entropy of 81.5 J/mol-K has been recommended. Recommended interaction parameters for the spinel-hercynite and forsterite-fayalite solutions are as follows:Spinel: W_{spinel-hercynite} = 9124.0 J/mol. W_{hercynite-spinel} = 0.0 J/molOlivine: W = 4500.0 J/mol for 1 cation.Excess entropies (on 1 cation basis) necessary to reproduce phase equilibria for the pyrope-almandine and almandine-grossular solutions are as follows:Mg-Fegarnet: W^s_{pyrope-almandine} = 11.760 − 0.00167 J/mol-K. W^s_{almandine-pyrope} = −10.146 +0.0037T J/mol-K.Fe-Ca garnet: W^s = −16.07 + 0.0126T J/mol-K.     

Modeling the thermodynamic parameters of six endmember garnets at ambient and high pressures from vibrational data

Raman and infrared spectroscopic data at ambient and high pressures were used to compute the lattice contribution to the heat capacities and entropies of six endmember garnets: pyrope, almandine, spessartine, grossular, andradite and uvarovite. Electronic, configurational and magnetic contributions are obtained from comparing available calorimetric data to the computed lattice contributions. For garnets with entropy in excess of the computed lattice contribution, the overwhelming majority is found in the subambient temperature regime. At room temperature, the non-lattice entropy is approximately 11.5 J/mol-K for pyrope, 49 J/mol-K for almandine, and 19 J/mol-K for andradite. The non-lattice entropy for pyrope and some for almandine cannot be accounted for by magnetic or electronic contributions and is likely to be configurational in nature. Estimates of low temperature non-lattice entropies for both spessartine and uvarovite are made in absence of calorimetric measurements and are based on low temperature calorimetry of other minerals containing the Mn²⁺ and Cr³⁺ cations as well as on solid solution garnets containing these cations. The estimate for uvarovite non-lattice entropy is approximately 18 J/mol-K, while for spessartine, approximately 45 J/mol-K. Neither of these cations is expected to provide electronic contributions to the entropy. For both iron-bearing garnets, a small electronic or magnetic entropy contribution continues above ambient temperatures. High pressure data on pyrope, grossular and andradite permit calculation of the thermodynamic parameters at high pressures, which are important for computation of processes in the Earth’s mantle. Thermal expansion coefficients of these materials were found to be 1.6, 1.5, 1.6×10⁻⁵ K⁻¹ at 298 K, respectively, using a Maxwell relation. These closely match the literature values at ambient conditions.     

Thermodynamic properties of MgSiO3 ilmenite from vibrational spectra

Unpolarized infrared (IR) reflectance spectra for MgSiO₃ ilmenite taken from a single-crystal and from a densly packed polycrystalline sample possessed all eight peaks mandated by symmetry between 337 and 850 cm^?1. Polarizations were inferred from intensity differences between the two samples. IR peak positions differ by up to 250 cm^?1 from recent calculations, but on average are within 11%. Heat capacity C _p calculated from these data by using a Kieffer-type model are within the experimental uncertainty of calorimetric measurements from 170 to 700 K. Outside this range, calculated C _p is probably accurate within a few percent, based on recent results for garnets. Calculated entropy is only slightly less accurate, giving S ⁰ (298.15 K) as 54.1 ±0.5 J/ mol-K, which is 10% lower than recent estimates based on phase equilibria. The slope of the phase boundary between ilmenite and perovskite is used to predict S ⁰ (298.15 K) of perovskite as 58.7 ±1.4 J/mol-K, which is 10% lower than previous values.     

29Si and 1H NMR spectroscopy of high-pressure hydrous magnesium silicates

We present NMR spectroscopic data, obtained by ¹H MAS, ¹H static spin-echo, and ²⁹Si{¹H} CP-MAS techniques, for a series of hydrous magnesium silicate samples synthesized at high pressure. This series includes chondrodite, β-Mg₂SiO₄, and phases A, B, superhydrous B, and E. Phases B and superhydrous B give very narrow ²⁹Si NMR peaks and display the most de-shielded Si^VI chemical shifts yet reported: ?170.4?ppm for B and ?166.6 for superhydrous B. The ¹H NMR spectra of B and superhydrous B confirm the presence of paired hydroxyls, as determined from refinement of the H positions from X-ray diffraction data. The ¹H MAS NMR spectra of phase B contain peaks for the two distinct hydrogen positions, with chemical shifts of +4.7 and +3.3?ppm. The static ¹H spectrum contains a powder pattern characteristic of a strongly coupled hydrogen pair, from which a dipolar coupling constant of 18.6(4)?kHz and inter-hydrogen distance of d(H–H)=1.86(2)?Å were obtained. Superhydrous B appears to give two poorly resolved ¹H MAS peaks, consistent with the presence of two distinct hydrogen pairs in the P2₁ mn crystal structure. Analysis of its spin-echo spectrum gives d(H–H)=1.83(3)?Å, slightly shorter than for phase B. β-Mg₂SiO₄, coexisting with phases B and superhydrous B, appears to give ²⁹Si{¹H} CP-MAS signal, indicating that it contains significant H concentration. The ²⁹Si chemical shifts for phases B, superhydrous B, and chondrodite, together with those reported previously for other Mg-silicates, show a good correlation with structural parameters.     

Structure and Mössbauer spectroscopy of barbosalite Fe2+Fe3+ 2 (PO4)2(OH)2 between 80 K and 300 K

Natural barbosalite Fe²⁺Fe³⁺ ₂ (PO₄)₂(OH)₂ from Bull Moose Mine, South Dakota, U.S.A., having ideal composition, was investigated with single crystal X-ray diffraction techniques, Mössbauer spectroscopy and SQUID magnetometry to redetermine crystal structure, valence state of iron and evolution of ⁵⁷Fe Mössbauer parameter and to propose the magnetic structure at low temperatures. At 298?K the title compound is monoclinic, space group P2₁/n, a _o ?= 7.3294(16)?Å, b _o ?=?7.4921(17)?Å, c _o ?=?7.4148 (18)?Å, β?=?118.43(3)°, Z?=?2. No crystallographic phase transition was observed between 298?K and 110?K. Slight discontinuities in the temperature dependence of lattice parameters and bond angles in the range between 150?K and 180?K are ascribed to the magnetic phase transition of the title compound. At 298?K the Mössbauer spectrum of the barbosalite shows two paramagnetic components, typical for Fe²⁺ and Fe³⁺ in octahedral coordination; the area ratio Fe³⁺/Fe²⁺ is exactly two, corresponding to the ideal value. Both the Fe²⁺ and the Fe³⁺ sublattice order magnetically below 173?K and exhibit a fully developed magnetic pattern at 160?K. The electric field gradient at the Fe²⁺ site is distorted from axial symmetry with the direction of the magnetic field nearly perpendicular to V_zz, the main component of the electric field gradient. The temperature dependent magnetic susceptibility exhibits strong antiferromagnetic ordering within the corner-sharing Fe³⁺-chains parallel to [101], whereas ferromagnetic coupling is assumed within the face-sharing [1?1?0] and [?1?1?0] Fe³⁺-Fe²⁺-Fe³⁺ trimer, connecting the Fe³⁺-chains to each other.     

Thermodynamics and crystal chemistry of the hematite–corundum solid solution and the FeAlO3 phase

High-temperature oxide-melt calorimetry and Rietveld refinement of powder X-ray diffraction patterns were used to investigate the energetics and structure of the hematite–corundum solid solution and ternary phase FeAlO₃ (with FeGaO₃ structure). The mixing enthalpies in the solid solution can be described by a polynomial ΔH_mix=WX _hem(1?X _hem) with W=116 ± 10 kJ mol^?1. The excess mixing enthalpies are too positive to reproduce the experimental phase diagram, and excess entropies in the solid solution should be considered. The hematite–corundum solvus can be approximately reproduced by a symmetric, regular-like solution model with ΔG _excess=(W _H ?TW _S )X _hem X _cor, where W _H= 116 ± 10 kJ mol^?1 and W _S =32 ± 4 J mol^?1 K^?1. In this model, short-range order (SRO) of Fe/Al is neglected because SRO probably becomes important only at intermediate compositions close to Fe:Al=1:1 but these compositions cannot be synthesized. The volume of mixing is positive for Al-hematite but almost ideal for Fe-corundum. Moreover, the degree of deviation from Vegard's law for Al-hematite depends on the history of the samples. Introduction of Al into the hematite structure causes varying distortion of the hexagonal network of oxygen ions while the position of the metal ions remains intact. Distortion of the hexagonal network of oxygen ions attains a minimum at the composition (Fe_0.95Al_0.05)₂O₃. The enthalpy of formation of FeAlO₃ from oxides at 298 K is 27.9 ± 1.8 kJ mol^?1. Its estimated standard entropy (including configurational entropy due to disorder of Fe/Al) is 98.9 J mol^?1 K^?1, giving the standard free energy of formation at 298 K from oxides and elements as +19.1 ± 1.8 and ?1144.2 ± 2.0 kJ mol^?1, respectively. The heat capacity of FeAlO₃ is approximated as C _p (T in K)= 175.8 ? 0.002472T ? (1.958 × 10⁶)/T ²? 917.3/T ^0.5+(7.546 × 10^?6) T ² between 298 and 1550 K, based on differential scanning calorimetric measurements. No ferrous iron was detected in FeAlO₃ by Mössbauer spectroscopy. The ternary phase is entropy stabilized and is predicted to be stable above about 1730 ± 70 K, in good agreement with the experiment. Static lattice calculations show that the LiNbO₃-, FeGaO₃-, FeTiO₃-, and disordered corundum-like FeAlO₃ structures are less stable (in the order in which they are listed) than a mechanical mixture of corundum and hematite. At high temperatures, the FeGaO₃-like structure is favored by its entropy, and its stability field appears on the phase diagram.     

Thermodynamic calculation of peridotite phase relations in the system MgO-Al2O3-SiO2-Cr2O3, with some geological applications

The system MgO-Al₂O₃-SiO₂(MAS) comprises 88–90% of the bulk composition of an average peridotite. The MAS ternary is thus a suitable starting point for exploring peridotite phase relations in multicomponent natural systems. The basic MAS phase relations may be treated in terms of the reactions (see list of symbols etc).

1. py (in Gt)=en (in Opx)+mats (in Opx),
2. en (in Opx)+sp (in Sp)=mats (in Opx)+fo (in Ol), and
3. py (in Gt)+fo (in Ol)=en (in Opx)+sp (in Sp).

Extensive reversed phase equilibria data on these three reactions by Danckwerth and Newton (1978), Perkins et al. (1981), and Gasparik and Newton (1984) employing identical experimental methods in the same laboratory have been used by us to deduce the following internally consistent thermodynamic data applying the technique of linear programming:ΔH ₂₉₈₍₁₎ ⁰ = 2536 J, ΔS ₂₉₈₍₁₎ ⁰ =? 6.064 J/K;ΔH ₂₉₈₍₂₎ ⁰ = 29435 J, ΔS ₂₉₈₍₂₎ ⁰ = 8.323 J/K; andΔH ₂₉₈₍₃₎ ⁰ =?26899 J, ΔS ₂₉₈₍₃₎ ⁰ =?14.388 J/K.These data are also found to be consistent with results of calorimetry. Figure 2 shows the calculated phase relations based on our thermodynamic data; they are consistent with the phase equilibria experiments. Successful extension of the MAS phase relations to multicomponent peridotites pivots on the extent to which the effects of the “non-ternary” (i.e. other than MAS) components can be quantitatively handled. Particularly hazardous in this context is Cr₂O₃, although it barely makes up 0.2 to 0.5 wt% of such rocks. This is because Cr⁺³ fractionates extremely strongly into Sp. This study focuses on the peridotite phase relations in the MgO-Al₂O₃-SiO₂-Cr₂O₃ (MASCr) quaternary. Thermodynamic calculations of the MASCr phase relations have been accomplished by using ΔH ₂₉₈ ⁰ and ΔS ₂₉₈ ⁰ values for the reactions (1) through (3) indicated above, in conjunction with data on thermodynamic mixing properties of

1. binary Sp (sp-pc) crystalline solution (Oka et al. 1984),
2. ternary Opx (en-mats-mcts) crystalline solution (this study), and
3. binary Gt (py-kn) crystalline solution (this study).

The results are shown in P-T projections (Figs. 3a and b) and isobaric-isothermal sections of MASCr in a projection through the component fo onto the SiO₂-Al₂O₃-Cr₂O₃ ternary (Figs. 4a and b). The most important results of this work may be summarized as follows:

1. With increasing incorporation of Cr⁺³ into Sp and Gt, the X _mats isopleths of the reactions (1) and (2) are shifted to higher temperatures (Fig. 3a); simultaneously, the spinel-peridotite to garnet-peridotite phase transition is moved to higher pressures (Fig. 3b).
2. At identical P and T, the X _mats values of Opx coexisting in equilibrium with Ol and Sp is strongly dependent upon the X _pc value in the latter phase (Figs. 4a and b). Accurate correction for the composition of Sp is, therefore, a necessary precondition for geothermometry of the spinelperidotites.
3. The discrepant temperatures reported by Sachtleben und Seck (1981, Fig. 5) from the spinel-peridotites of the Eifel area (systematically too high temperatures as a function of X _pc in Sp) are demonstrated to be the result of ignoring the nonideality in the chromian spinels.

     

The high-temperature heat capacity of natural calcite (CaCO3)

The heat capacity (C _P) of a natural sample of calcite (CaCO₃) has been measured from 350 to 775 K by differential scanning calorimetry (DSC). Heat capacities determined for a powdered sample and a single-crystal disc are in close agreement and have a total uncertainty of ±1 percent. The following equation for the heat capacity of calcite from 298 to 775 K was fit by least squares to the experimental data and constrained to join smoothly with the low-temperature heat capacity data of Staveley and Linford (1969) (C _P in J mol^?1 K^?1, T in K): $$\begin{gathered} C_p = - 184.79 + 0.32322T - 3,688,200T^{ - 2} \hfill \\ {\text{ }} - (1.2974{\text{ }} \times {\text{ 10}}^{ - {\text{4}}} )T^2 + 3,883.5T^{ - 1/2} \hfill \\ \end{gathered} $$ Combining this equation with the S ₂₉₈ ⁰ value from Staveley and Linford (1969), entropies for calcite are calculated and presented to 775 K. A simple method of extrapolating the heat capacity function of calcite above 775 K is presented. This method provides accurate entropies of calcite for high-temperature thermodynamic calculations, as evidenced by calculation of the equilibrium: CaCO_{3 (s)}=CaO_(s)+CO_{2 (s)}.     

Single-crystal elastic properties of chondrodite: implications for water in the upper mantle

Chondrodite, a member of the humite group of minerals, forms by hydration of olivine and is stable over a range of temperatures and pressures that includes a portion of the uppermost mantle. We have measured the single crystal elastic properties of a natural chondrodite specimen at ambient conditions using Brillouin spectroscopy. The isotropic aggregate bulk (K) and shear (μ) moduli calculated from the single-crystal elastic moduli, C_ij, are: K_S=118.4(16) GPa and μ=75.6(7) GPa. A comparison of the structures and elasticity of olivine and chondrodite indicate that the replacement of O with (OH,F) in M²⁺O₆ octahedra has a small effect on the elasticity of humite-group minerals. The slightly diminished elastic moduli of humite-group minerals (as compared to olivine) are likely caused by a smaller ratio of strong structural elements (SiO₄ tetrahedra) to weaker octahedra, and perhaps a more flexible geometry of edge-sharing MO₄(O,OH,F)₂ octahedra. In contrast to the humite-olivine group minerals, the incorporation of water into garnets and spineloids leads to a more substantial decrease in the elastic properties of these minerals. This contrasting behavior is due to formation of O₄H₄ tetrahedra and vacant hydroxyl-bearing octahedra in the garnets and spineloids, respectively. Therefore, the mechanism of incorporation of H/OH into mineral phases, not only degree of hydration, should be taken into account when estimating the effect of water on the elastic properties of minerals. The bulk elastic wave velocities of chondrodite and olivine are very similar. If humite-like incorporation of OH is predominant in the upper mantle, then the reaction of OH with olivine will have a minor or possibly no detectable effect on seismic velocities. Thus, it may be difficult to distinguish chondrodite-bearing rocks from “anhydrous” mantle on the basis of seismically determined velocities for the Earth. Received: 25 February 1998 / Revised, accepted: 18 August 1998     

The 57Fe Mössbauer parameters of pyrite and marcasite with different provenances

Eighteen pyrite and twelve marcasite samples which have different provenances have been investigated to determine the systematics of the influence of mineralogical and geological factors on the ⁵⁷Fe Mössbauer spectra at 298 K. The following results have been obtained: there is no ambiguity in distinguishing single phase pyrite from single phase marcasite by means of ⁵⁷Fe Mössbauer spectroscopy at 298 K. At 298 K the average electric quadrupole splitting, 〈ΔE_Q〉, and average isomer shift, 〈δ〉, with respect to Fe metal, are 0.6110 ± 0.0030 mm s^?1 and 0.313 ± 0.008 mm s^?1, respectively, for the 18 pyrites; 〈ΔE_Q〉 = 0.5030 ± 0.0070 mm s^?1 and 〈δ〉 = 0.2770 ± 0.0020 mm s^?1 for the 12 marcasites. At 77 K, ΔE_Q is 0.624 mm s^?1 for pyrite and 0.508 mm s^?1 for marcasite. In distinguishing pyrites from marcasites, spectra obtained at 77 K are not warranted.The Mössbauer parameters of pyrite and marcasite exhibit appreciable variations, which bear no simple relationship to the geological environment in which they occur but appear to be selectively influenced by impurities, especially arsenic, in the pyrite lattice. Quantitative and qualitative determinations of pyrite/marcasite mechanical mixtures are straightforward at 298 K and 77 K but do require least-squares computer fittings and are limited to accuracies ranging from ±5 to ±15 per cent by uncertainties in the parameter values of the pure phases. The methodology and results of this investigation are directly applicable to coals for which the presence and relative amounts of pyrite and marcasite could be of considerable genetic significance.     

Thermal expansion of hydrated six-coordinate silicon in thaumasite,Ca<Subscript>3</Subscript>Si(OH)<Subscript>6</Subscript>(CO<Subscript>3</Subscript>)(SO<Subscript>4</Subscript>)·12H<Subscript>2</Subscript>O

Thaumasite, Ca₃Si(OH)₆(CO₃)(SO₄)12H₂O, occurs as a low-temperature secondary alteration phase in mafic igneous and metamorphic rocks, and is recognized as a product and indicator of sulfate attack in Portland cement. It is also the only mineral known to contain silicon in six-coordination with hydroxyl (OH)^? that is stable at ambient P–T conditions. Thermal expansion of the various components of this unusual structure has been determined from single-crystal X-ray structure refinements of natural thaumasite at 130 and 298 K. No phase transitions were observed over this temperature range. Cell parameters at room temperature are: a= 11.0538(6) Å, c=10.4111(8) Å and V=1101.67(10) ų, and were measured at intervals of about 50 K between 130 and 298 K, resulting in mean axial and volumetric coefficients of thermal expansion (×10^?5K^?1); α _a =1.7(1), α _c =2.1(2), and α _V =5.6(2). Although the unit cell and ^VIIICaO₈ polyhedra show significant positive thermal expansion over this temperature range, the silicate octahedron, sulfate tetrahedron, and carbonate group show zero or negative thermal expansion, with α _V (^VISiO₆) = ?0.6 ± 1.1, α _V (^IVSO₄)=?5.8 ± 1.4, and α _R (C–O)= 0.0 ± 1.8 (×10^?5 K^?1). Most of the thermal expansion is accommodated by lengthening of the R(O...O) hydrogen bond distances by on average 5σ, although the hydrogen bonds involving hydroxyl sites on ^VISi expand twice as much as those on molecular water, causing the [Ca₃Si(OH)₆(H₂O)₁₂]⁴⁺ columns to expand in diameter more than they move apart over this temperature range. The average Si–OH bond length of the six-coordinated Si atom 〈R(^VISi–OH)〉 in thaumasite is 1.783(1) Å, being about 0.02 Å (?20σ) shorter than ^VISi–OH in the dense hydrous magnesium silicate, phase D, MgSi₂H₂O₆.     

Solubility of ettringite (Ca6[Al(OH)6]2(SO4)3 · 26H2O) at 5–75°C

The solubility of ettringite (Ca₆[Al(OH)₆]₂(SO₄)₃ · 26H₂O) was measured in a series of dissolution and precipitation experiments at 5–75°C and at pH between 10.5 and 13.0 using synthesized material. Equilibrium was established within 4 to 6 days, with samples collected between 10 and 36 days. The log K_SP for the reaction Ca₆[Al(OH)₆]₂(SO₄)₃ · 26H₂O ⇌ 6Ca²⁺ + 2Al(OH)₄⁻ + 3SO₄²⁻ + 4OH⁻ + 26H₂O at 25°C calculated for dissolution experiments (−45.0 ± 0.2) is not significantly different from the log K_SP calculated for precipitation experiments (−44.8 ± 0.4) at the 95% confidence level. There is no apparent trend in log K_SP with pH and the mean log K_SP,298 is −44.9 ± 0.3. The solubility product decreased linearly with the inverse of temperature indicating a constant enthalpy of reaction from 5 to 75°C. The enthalpy and entropy of reaction ΔH^°_r and ΔS^°_r, were determined from the linear regression to be 204.6 ± 0.6 kJ mol⁻¹ and 170 ± 38 J mol⁻¹ K⁻¹. Using our values for log K_SP, ΔH^°_r, and ΔS^°_r and published partial molal quantities for the constituent ions, we calculated the free energy of formation ΔG^°_f,298, the enthalpy of formation ΔH^°_f,298, and the entropy of formation ΔS^°_f,298 to be −15211 ± 20, −17550 ± 16 kJ mol⁻¹, and 1867 ± 59 J mol⁻¹ K⁻¹. Assuming ΔC_P,r is zero, the heat capacity of ettringite is 590 ± 140 J mol⁻¹ K⁻¹.     

Solubility of Ca6[Al(OH)6]2(CrO4)3·26H2O,the chromate analog of ettringite; 5–75°C

Ca₆[Al(OH)₆]₂(CrO₄)₃·26H₂O, the chromate analog of the sulfate mineral ettringite, was synthesized and characterized by X-ray diffraction, Fourier transform infra-red spectroscopy, thermogravimetric analyses, energy dispersive X-ray spectrometry, and bulk chemical analyses. The solubility of the synthesized solid was measured in a series of dissolution and precipitation experiments conducted at 5–75°C and at initial pH values between 10.5 and 12.5. The ion activity product (IAP) for the reaction Ca₆[Al(OH)₆]₂(CrO₄)₃·26H₂O⇌6Ca²⁺+2Al(OH)⁻₄+3CrO²⁻₄+4OH⁻+26H₂O varies with pH unless a CaCrO_4(aq) complex is included in the speciation model. The log K for the formation of this complex by the reaction Ca²⁺+CrO²⁻₄=CaCrO_4(aq) was obtained by minimizing the variance in the IAP for Ca₆[Al(OH)₆]₂(CrO₄)₃·26H₂O. There is no significant trend in the formation constant with temperature and the average log K is 2.77±0.16 over the temperature range 5–75°C. The log solubility product (log K_SP) of Ca₆[Al(OH)₆]₂(CrO₄)₃·26H₂O at 25°C is −41.46±0.30. The temperature dependence of the log K_SP is log K_SP=A−B/T+D log(T) where A=498.94±48.99, B=27,499±2257, and D=−181.11±16.74. The values of ΔG⁰_r,298 and ΔH⁰_r,298 for the dissolution reaction are 236.6±3.9 and 77.5±2.4 kJ mol⁻¹. the values of ΔC⁰_P,r,298 and ΔS⁰_r,298 are −1506±140 and −534±83 J mol⁻¹ K⁻¹. Using these values and published standard state partial molal quantities for constituent ions, ΔG⁰_f,298=−15,131±19 kJ mol⁻¹, ΔH⁰_f,298=−17,330±8.6 kJ mol⁻¹, ΔS⁰₂₉₈=2.19±0.10 kJ mol⁻¹ K⁻¹, and ΔC⁰_Pf,298=2.12±0.53 kJ mol⁻¹ K⁻¹, were calculated.     

Vibrational mode analysis and heat capacity calculation of K2SiSi3O9-wadeite

The phonon dispersions and vibrational density of state (VDoS) of the K₂SiSi₃O₉-wadeite (Wd) have been calculated by the first-principles method using density functional perturbation theory. The vibrational frequencies at the Brillouin zone center are in good correspondence with the Raman and infrared experimental data. The calculated VDoS was then used in conjunction with a quasi-harmonic approximation to compute the isobaric heat capacity (C _P ) and vibrational entropy ( $S_{298}^{0}$ ), yielding C _P (T) = 469.4(6) ? 2.90(2) × 10³  T ^?0.5 ? 9.5(2) × 10⁶  T ^?2 + 1.36(3) × 10⁹  T ^?3 for the T range of 298–1,000 K and $S_{298}^{0}$  = 250.4 J mol^?1 K^?1. In comparison, these thermodynamic properties were calculated by a second method, the classic Kieffer’s lattice vibrational model. On the basis of the vibrational mode analysis facilitated by the first-principles simulation result, we developed a new Kieffer’s model for the Wd phase. This new Kieffer’s model yielded C _P (T) = 475.9(6) ? 3.15(2) × 10³  T ^?0.5 – 8.8(2) × 10⁶  T ^?2 + 1.31(3) × 10⁹  T ^?3 for the T range of 298–1,000 K and $S_{298}^{0}$  = 249.5(40) J mol^?1 K^?1, which are in good agreement both with the results from our first method containing the component of the first-principles calculation and with some calorimetric measurements in the literature.     

Crystallographic phase transition and valence fluctuation in synthetic mn-bearing ilvaite CaFe2+ 2-x Mn2+ xFe3+ [Si2O7/O/(OH)]

The dependence of the electronic and the crystallographic structure on temperature of synthetic Mnbearing ilvaites CaFe²⁺ _2-xMn²⁺ _xFe³⁺ [Si₂O₇/O/OH] with 0≤x≤0.19 has been investigated. The change of the electronic structure was studied by ⁵⁷Fe Mössbauer spectroscopy. The spectra show an increasing valence fluctuation rate between Fe²⁺ and Fe³⁺ in the double chain of edge-sharing octahedra with increasing temperature resulting in a mixed valent state of iron. The valence fluctuation rate is distinctly increased by the Mnsubstitution. The temperature of the crystallographic phase transition T _x as studied by a high temperature Guinier method is distinctly lowered by the Mn-substitution (x = 0.0, T _x=390K; x = 0.12, T _x =370K; x = 0.19, T _x=295K). The reasons for this behaviour are discussed in terms of Fe^{2 +}, Fe^{3 +} cation order-disorder, electronic relaxation rate, and relaxation of the lattice. In the monoclinic phase there is electron hopping between Fe^{2 +}, Fe^{3 +} pairs whereas in the orthorhombic phase there is extended electron delocalization via a narrow, d-band mechanism.     

Revised values for the Gibbs free energy of formation of [Al(OH)4 aq−], diaspore,boehmite and bayerite at 298.15 K and 1 bar,the thermodynamic properties of kaolinite to 800 K and 1 bar,and the heats of solution of several gibbsite samples

Solution calorimetric measurements compared with solubility determinations from the literature for the same samples of gibbsite have provided a direct thermochemical cycle through which the Gibbs free energy of formation of [Al(OH)_{4 aq}^?] can be determined. The Gibbs free energy of formation of [Al(OH)_{4 aq}^?] at 298.15 K is ?1305 ± 1 kJ/mol. These heat-of-solution results show no significant difference in the thermodynamic properties of gibbsite particles in the range from 50 to 0.05 μm.The Gibbs free energies of formation at 298.15 K and 1 bar pressure of diaspore, boehmite and bayerite are ?9210 ± 5.0, ?918.4 ± 2.1 and ?1153 ± 2 kJ/mol based upon the Gibbs free energy of [A1(OH)_{4 aq}^?] calculated in this paper and the acceptance of ?1582.2 ± 1.3 and ?1154.9 ± 1.2 kJ/mol for the Gibbs free energy of formation of corundum and gibbsite, respectively.Values for the Gibbs free energy formation of [Al(OH)_{2 aq}⁺] and [AlO_{2 aq}^?] were also calculated as ?914.2 ± 2.1 and ?830.9 ± 2.1 kJ/mol, respectively. The use of [AlC_{2 aq}^?] as a chemical species is discouraged.A revised Gibbs free energy of formation for [H₄SiO_4aq⁰] was recalculated from calorimetric data yielding a value of ?1307.5 ± 1.7 kJ/mol which is in good agreement with the results obtained from several solubility studies.Smoothed values for the thermodynamic functions C_P⁰, ($\text{H}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, $\text{(}\text{G}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, S_T⁰ - S₀⁰, $\text{ΔH}{}_{\mathrm{?,298}}{}^0$ kaolinite are listed at integral temperatures between 298.15 and 800 K. The heat capacity of kaolinite at temperatures between 250 and 800 K may be calculated from the following equation: C_P⁰ = 1430.26 ? 0.78850 T + 3.0340 × 10^?4T² ?1.85158 × 10^?4T²$\text{1}\text{2}\text{+ 8.3341 × 10}{}^6\text{T}{}^{\mathrm{?2}}$.The thermodynamic properties of most of the geologically important Al-bearing phases have been referenced to the same reference state for Al, namely gibbsite.     

Low T heat capacity measurements and new entropy data for titanite (sphene): implications for thermobarometry of high-pressure rocks

The accepted standard state entropy of titanite (sphene) has been questioned in several recent studies, which suggested a revision from the literature value 129.3 ± 0.8 J/mol K to values in the range of 110–120 J/mol K. The heat capacity of titanite was therefore re-measured with a PPMS in the range 5 to 300 K and the standard entropy of titanite was calculated as 127.2 ± 0.2 J/mol K, much closer to the original data than the suggested revisions. Volume parameters for a modified Murgnahan equation of state: V _P,T  = V ₂₉₈° × [1 + a°(T − 298) − 20a°(T − 298)] × [1 – 4P/(K ₂₉₈ × (1 – 1.5 × 10⁻⁴ [T − 298]) + 4P)]^1/4 were fit to recent unit cell determinations at elevated pressures and temperatures, yielding the constants V ₂₉₈° = 5.568 J/bar, a° = 3.1 × 10⁻⁵ K⁻¹, and K = 1,100 kbar. The standard Gibbs free energy of formation of titanite, −2456.2 kJ/mol (∆H°_f = −2598.4 kJ/mol) was calculated from the new entropy and volume data combined with data from experimental reversals on the reaction, titanite + kyanite = anorthite + rutile. This value is 4–11 kJ/mol less negative than that obtained from experimental determinations of the enthalpy of formation, and it is slightly more negative than values given in internally consistent databases. The displacement of most calculated phase equilibria involving titanite is not large except for reactions with small ∆S. Re-calculated baric estimates for several metamorphic suites yield pressure differences on the order of 2 kbar in eclogites and 10 kbar for ultra-high pressure titanite-bearing assemblages.     

The heat capacity of a natural monticellite and phase equilibria in the system CaO-MgO-SiO2-CO2

The heat capacity of a natural monticellite (Ca_1.00Mg_.09Fe_.91Mn_.01Si_0.99O_3.99) measured between 9.6 and 343 K using intermittent-heating, adiabatic calorimetry yields C_p⁰(298) and S₂₉₈⁰ of 123.64 ± 0.18 and 109.44 ± 0.16 J · mol⁻¹K⁻¹ respectively. Extrapolation of this entropy value to end-member monticellite results in an S⁰₂₉₈ = 108.1 ± 0.2 J · mol⁻¹K⁻¹. High-temperature heat-capacity data were measured between 340–1000 K with a differential scanning calorimeter. The high-temperature data were combined with the 290–350 K adiabatic values, extrapolated to 1700 K, and integrated to yield the following entropy equation for end-member monticellite (298–1700 K): S_T⁰(J · mol⁻¹K⁻¹) = S₂₉₈⁰ + 164.79 In T + 15.337 · 10⁻³T + 22.791 · 10⁵T⁻² − 968.94. Phase equilibria in the CaO-MgO-SiO₂ system were calculated from 973 to 1673 K and 0 to 12 kbar with these new data combined with existing data for akermanite (Ak), diopside (Di), forsterite (Fo), merwinite (Me) and wollastonite (Wo). The location of the calculated reactions involving the phases Mo and Fo is affected by their mutual solid solution. A best fit of the thermodynamically generated curves to all experiments is made when the S⁰₂₉₈ of Me is 250.2 J · mol⁻¹ K⁻¹ less than the measured value of 253.2 J · mol⁻¹ K⁻¹.A best fit to the reversals for the solid-solid and decarbonation reactions in the CaO-MgO-SiO₂-CO₂ system was obtained with the ΔG⁰₂₉₈ (kJ · mole⁻¹) for the phases Ak(−3667), Di(−3025), Fo(−2051), Me(−4317) and Mo(−2133). The two invariant points − Wo and −Fo for the solid-solid reactions are located at 1008 ± 5 K and 6.3 ± 0.1 kbar, and 1361 ± 10 K and 10.2 ± 0.2 kbar respectively. The location of the thermodynamically generated curves is in excellent agreement with most experimental data on decarbonation equilibria involving these phases.